Logiweb aspects of lemma negativeLessPositive in pyk

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The predefined "pyk" aspect

define pyk of lemma negativeLessPositive as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small n unicode small e unicode small g unicode small a unicode small t unicode small i unicode small v unicode small e unicode capital l unicode small e unicode small s unicode small s unicode capital p unicode small o unicode small s unicode small i unicode small t unicode small i unicode small v unicode small e unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma negativeLessPositive as text unicode start of text unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small i unicode small v unicode small e unicode capital l unicode small e unicode small s unicode small s unicode capital p unicode small o unicode small s unicode small i unicode small t unicode small i unicode small v unicode small e unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma negativeLessPositive as system Q infer all metavar var x end metavar indeed not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer not0 - metavar var x end metavar <= metavar var x end metavar imply not0 not0 - metavar var x end metavar = metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma negativeLessPositive as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer prop lemma first conjunct modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude 0 <= metavar var x end metavar cut lemma leqAddition modus ponens 0 <= metavar var x end metavar conclude 0 + - metavar var x end metavar <= metavar var x end metavar + - metavar var x end metavar cut lemma plus0Left conclude 0 + - metavar var x end metavar = - metavar var x end metavar cut axiom negative conclude metavar var x end metavar + - metavar var x end metavar = 0 cut lemma subLeqLeft modus ponens 0 + - metavar var x end metavar = - metavar var x end metavar modus ponens 0 + - metavar var x end metavar <= metavar var x end metavar + - metavar var x end metavar conclude - metavar var x end metavar <= metavar var x end metavar + - metavar var x end metavar cut lemma subLeqRight modus ponens metavar var x end metavar + - metavar var x end metavar = 0 modus ponens - metavar var x end metavar <= metavar var x end metavar + - metavar var x end metavar conclude - metavar var x end metavar <= 0 cut lemma leqLessTransitivity modus ponens - metavar var x end metavar <= 0 modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude not0 - metavar var x end metavar <= metavar var x end metavar imply not0 not0 - metavar var x end metavar = metavar var x end metavar end quote state proof state cache var c end expand end define